In the prior art, the actuator comprises an articulated quadrilateral mechanism (typically an articulated parallelogram) with four connecting rods hinged together according to four pin axes by four pin elements, in which the first connecting rod is integrally fixed to the bicycle frame, the second connecting rod (opposite to the first connecting rod in the articulated quadrilateral) is fixed to a support for the gear-shift derailleur; the deformation of the articulated quadrilateral determines the displacement of the derailleur and therefore the gear-change.